Question

If $A(-2,-1), B(4,0), C(3,3)$ and $D(-3,2)$ are the vertices of a parallelogram, then
Statement I Slope of $A B=$ Slope of $B C$ and
Slope of $C D=$ Slope of $A D$.
Statement II Mid-point of $A C=$ Mid- point of $B D$.

• A. Both statements are true
• B. Statement I is true and Statement II is false
• C. Statement I is false and Statement II is true
• D. Both statements are false

Answer 1

Answer: (C)

$\because A B C D$ is a parallelogram.
$\therefore A B \| C D \Rightarrow$ Slope of $A B=$ Slope of $C D$
and $B C \| AD \rightarrow$ Slope of $B C=$ Slope of $AD$
Hence, Statement $I$ is false.
Now, mid-point of $A C=\left(\frac{-2+3}{2}, \frac{-1+3}{2}\right)$
$=\left(\frac{1}{2}, \frac{2}{2}\right)=\left(\frac{1}{2}, 1\right)$
and mid-point of $B D=\left(\frac{4-3}{2}, \frac{0+2}{2}\right)=\left(\frac{1}{2}, 1\right)$
$\Rightarrow$ Mid-point of $A C=$ Mid-point of $B D$
Hence, Statement II is true.